Low Temperature X-ray Detectors

Caroline K. StahleNASA / Goddard Space Flight Center

• Motivation for low temperature x-ray detectors

• The two approaches to “non-dispersive” spectroscopy

• Superconducting tunnel junctions for the x-ray regime

• Micro-calorimeters and their operating principles• resistive thermometers• magnetic thermometers

• Cooling

• LTDs and x-ray astronomy: past, present, and future

• Summary and comparisons

Outline:

•The good energy resolution of grating spectrometers requires optics with very high angular resolution, but the design of x-ray telescopes involves a trade-off between angular resolution and collecting area, tending to put gratings at a sensitivity disadvantage.

• Gratings multiplex by dispersing the spectrum across a position sensitive detector, but at the expense of confusion in spectra from spatially extended objects.

Motivation: high resolution with a non-dispersive x-ray spectrometer

• The 0.1 – 10 keV x-ray band corresponds to temperatures from 106 to108 K. At these temperatures the dominant radiation is collisionally-excited characteristic lines of partially ionized heavy elements. These lines provide a wealth of diagnostics on the elemental abundances and physical conditions in the gas, and measurements of Doppler shifts and line widths can give valuable information about the motion.

How can we directly measure the energy of an x-ray photon?

We can do either an equilibrium or a non-equilibrium measurement.

Now, a pretty basic question:

• Absorbed energy goes into quantized excitations.• Each excitation has energy much greater than kT. • These excitations are then counted to determine the energy. • Since, invariably, some of the energy goes elsewhere, such as into heat, the ultimate energy resolution is determined by the statistics governing the partition of energy between the system of excited states and everything else.

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dE∝ N N

Non-equilibrium:

• This is how most photon and particle detectors work. • In order to improve the measurement statistics, a large number of excitation quanta is required. • This, in turn, requires low temperature operation.

• The energy is deposited in an isolated thermal mass.• The resulting increase in temperature is measured. • At the time of the measurement, all of the deposited energy has become heat and the sensor is in thermal equilibrium. • The ultimate energy resolution is determined by how well one can measure this change in temperature against a background of thermodynamically unavoidable temperature fluctuations. • This is calorimetry. • Low temperature operation is required in order to minimize these thermodynamic energy fluctuations.

Equilibrium:

• Excitations from the superconducting ground state are called quasiparticles.

•The gap between the ground state and the lowest excited states is ~1 meV for many superconductors.

• Compared with a semiconductor with bandgap ~ 1 eV, a superconducting non-equilibrium energy sensor should provide much higher energy resolution, provided the temperature is low enough to render thermal excitation of the quasiparticles improbable.

• The most efficient way to measure the quasiparticle density is through measuring the quasiparticle tunneling current from the absorbing superconductor through an insulating barrier to a superconducting collection electrode. The Josephson pair tunneling current must be suppressed by a magnetic field.

Superconducting Tunnel Junctions (STJ)

quasiparticle

Cooper pair

quasiparticle diffusion

quasiparticle emitsphonon, becomestrapped

emitted phononbreaks additionalpair

quasiparticles broken as result of x-ray absorption

SUPERCONDUCTOR USEDAS X-RAY ABSORBER

SUPERCONDUCTORWITH NARROW GAP

SUPERCONDUCTOR

Fermi level

tunneling

Fermi level

backtunneling

Al2O3

≈100 × 100 µmSiO2 Nb

(165 )Nb Absorber nmAl Si Substrate

SiO2 AlNb

- X ray Photon

S. Friedrich -- LLNL

STJ schematic and array

Limiting Energy Resolution for a Tunnel Junction:

Fano limit (no quasiparticle multiplication)

Backtunneling limit

(where F~ 0.2 is the Fano factor and <n> is the average backtunneling multiplier)

dE FWHM =2.355 1.7ΔEF

dE FWHM =2.355 1.7ΔE F + 1+1n

⎛

⎝ ⎜ ⎜

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Superconductorused asabsorber

∆(energy gap)

Theoretical∆E at 6 keV(singletunneling)

Theoretical∆E at 6 keV(multipletunneling)

∆E Achievedat 6 keV

Niobium 1.52 meV 4.3 eV 10.6 eV 24 eV (LLNL)

Tantalum 0.71 meV 2.9 eV 7.2 eV 13 eV (Yale)

Aluminum 0.17 meV 1.4 eV 3.5 eV 12 eV (T. U. Munich)

Titanium 0.052 meV 0.8 eV 2.0 eV

Hafnium 0.017 meV 0.46 eV 1.1 eV

STJ performance in the x-ray regime:

Yale STJ Imager

One can achieve position resolution comparable to energy resolution, since we determine position from the charge division.

D. Prober

About 150 years ago, James Joule and Julius von Mayer independently determined that HEAT = ENERGY, and calorimetry was born.

But, only about 19 years ago, the power of performing calorimetric measurements at very low temperatures (< 0.1 K) was realized, independently, by Harvey Moseley and by Etorre Fiorini and Tapio Niinikoski. This is called MICROCALORIMETRY, or occasionally QUANTUM CALORIMETRY, because of its ability to measure the energy of individual photons or particles with high sensitivity.

Calorimetry is OLD!

Some thermometers:• resistive• capacitive• inductive• paramagnetic• electron tunneling • thermoelectric

Calorimeters

• Low temperature• Sensitive thermometer• Thermal link weak enough that the time for restoration of the base temperature is the slowest time constant in the system yet not so weak that the device is made too slow to handle the incident flux. • Absorber with high cross section yet low heat capacity• Reproducible and efficient thermalization

Basic calorimeter requirements:

dErms = kT2CThermal fluctuation noise =

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Signal (with thermalization time)Phonon noiseWhite noise

To answer this question, we need to specify the kind of thermometer. The best energy resolution, so far, has been obtained with resistor-based calorimeters, both semiconductor thermistors (the pioneering technology) and superconducting transition-edge sensors.

dT ––> dR Sensitivity = d log R / d log T

Considerations for resistive thermometers:• All resistors have Johnson noise. • In order to measure the change in resistance as a change in current or voltage, the sensor must be electrically biased, resulting in Joule heating.

How well can a microcalorimeter measure energy?

Moseley, Mather, and McCammon (1984) worked out the ultimate energy resolution attainable with an ideal resistor-based microcalorimeter. We can understand the basic dependencies simply by understanding how the signal-to-noise and bandwidth change with , T, and C.

dE ∝T C / α

dE=ξ kT2CThis looks a lot like the RMS thermal fluctuation noise! But note, there is no reason why can’t be < 1!

Electrothermal Feedback

PJoule = I2R(T) = V2/R(T)

For dP/dT < 0 (negative feedback):if dR/dT < 0, we want (nearly) constant current bias.if dR/dT > 0, we want (nearly) constant voltage bias.

Negative electrothermal feedback literally speeds up the cooling of a microcalorimeter after an impulse of energy. For sensitive thermistors (large | |), this can be a very important effect. It doesn’t change the signal-to-noise anywhere, but it does permit pushing the pulse decay times up against the limiting thermalization time, making most efficient use of the available bandwidth.

• ion-implanted Si and neutron transmutation doped (NTD) Ge• doped within the metal-insulator transition• conduction proceeds via thermally activated jumps of isolated charge carriers between impurity levels. The mechanism is called variable range hopping (VRH). The average hopping distance increases as the temperature is lowered, as it becomes more probable for an electron to tunnel further to a site requiring less change in energy than to tunnel to a nearby site with a difference in energy large compared to that available in the spectrum of phonons. In doped crystalline semiconductors, which have a Coulomb gap in the density of states, VRH produces the resistance law:

R =R0 exp T0 T( )

Semiconductor thermistors:

Insulators and semiconductors impurity levels in their bandgaps on which electrons can become trapped before thermalizing, leading to incomplete and noisy thermalization

Normal metals thermalize well, but the electronic specific heat is prohibitive Narrow gap semiconductors / semimetals (HgTe) thermalize well, but have low Debye temperatures (high specific heat) High Z superconductorspoor thermalization in superconductors with high Debye temperatures

HgTe and Sn have been good compromises.

Absorbers for use with semiconductor thermistors:• low heat capacity (< 0.1 pJ/K if limited to α< 6 and needing few eV resolution)• high Z constituents (for X-ray opacity)• good thermalization

State of the art in NTD-based x-ray calorimeters:

Milan:Sn absorber

SAO: Comparable results with similar materials

Single devices and small (e.g 4-pixel) arrays. Microlithographic processes available for arraying in Si not yet developed for NTD Ge.

State of the art in astrophysical instrumentation using x-ray calorimeter arrays: XRS (Astro-E) and XQC (sounding rocket):

Micromachined arrays of ion-implanted Si with HgTe absorbers optimized for the 0.3 - 10 keV and < 1 keV x-ray bands respectively• Goddard 36-pixel array flown on Wisconsin/GSFC XQC sounding rocket experiment, had an energy resolution ranging from 5 to about 12 eV over the 0.05 - 1 keV band.• Goddard 32-pixel XRS array: 8-9 eV at low energies and 11-12 eV at 6 keV.

(more about both of these later….)

The dominant noise term in the XRS devices is excess 1/f noise that prevents the realization of the theoretical performance; however, preliminary results from experiments with a novel fabrication technique indicate that it will soon be possible to combine the advantages of working with silicon for array fabrication with the uniform doping and lower excess noise associated with the NTD thermistors.

Diffusing implanted dopants confined in a “silicon-on-insulator” layer has already yielded deeper and more uniform implant density than had previously been possible, and this has resulted in the elimination of the excess noise term.

Preliminary data indicated that it should be possible to make an XRS-style array with no worse than 9 eV resolution at 6 keV, and possibly as good as 4 eV.

Stay tuned: we may be able qualify this technology in time for XRS-2!

Superconducting Transition-Edge Sensors in Calorimeters

R = 0

R = Rn

The transition is not a step function. Within the transition, the sensor isa very sensitive thermometer.

increasing T ⇒

What causes the resistance in the transition?

• thermal gradient leads to “phase separation”

OR

• flux flow (e.g. nucleation of phase-slip lines)

• Thus we can no longer improve resolution by increasing sensitivity.

• For 6 keV x-rays, the predicted resolution works out to be nearly the same as that originally anticipated for semiconductor calorimeters (that is, a few eV).

• But the large heat capacity budget eases absorber selection and has other practical advantages.

• And the large α, through electrothermal feedback, permits the falltime to be shortened to match the measurement bandwidth, reducing pile-up

• For lower saturation energies, such as for an optical detector, the full advantage of the higher sensitivity can be exploited

dE∝TC/α

TES thermometers provide ~100 times more sensitivity than practical semiconductor thermistors.

• Increase α, increase the measurement bandwidth.

• Except, this α is only good over a small temperature range.

• We need to increase C to stay within the transition. This C is set by α and the required saturation energy. C = E/dT ~ αE/T

1480 1485 1490 1495 1500 15050

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Instrument Resolution:

2.0 0.1 eV FWHMAl Kα1,2

Al Kα3,4

Bismuth absorber

TES Al/Ag bilayer

450 counts/sec

K. Irwin

SRON Ti/Au TES with Cu absorber, 3.9 eV FWHM, 100 s time constant, 5 minute acquisition time. Line broadens to 4.5 eV FWHM for 30 minute acquisition.

FWHM = 3.9 eV

H. Hoevers - SRON

Goddard Mo/Au TES:2.4 +/- 0.2 eV at 1.5 keV and 3.7 +/- 0.2 eV at 3.3 keV.

Al Kαinto 300 x 300 micron TES

K Kαinto 500 x 500 micron TES

Paramagnetic calorimeters (< 1eV resolution at 6 keV predicted)• spin system of isolated ions of d and f transition elements in a non-magnetic matrix. • in a weak magnetic field there exists a small Zeeman splitting between the spin-up and spin-down energy states, thus a temperature change results in a change in magnetization, which can be sensed by a SQUID• because the sensitivity increases with the heat capacity of the spin system, the predicted resolution of an optimized magnetic calorimeter degrades more slowly with heat capacity than resistive calorimeters• What ends up being the bandwidth limiting noise without Johnson noise? SQUID noise, pick-up from Johnson noise currents in absorber and nearby metal, phonon noise between weakly coupled systems

Thermometers not based on changing resistance:

• no dissipation, but also no electrothermal feedback• no Johnson noise tied directly to the thermometric property of the sensor

Au:Er Heidelberg/Brown13 eV FWHM at 5.9 keV

Position Sensing CalorimeterPosition Sensing CalorimeterSegmented metallic absorbers between Mo/Au TES sensors

• For x-ray applications, the energy resolution required is 10-100 times higher than the spatial resolution required. In that context, it doesn’t make sense to squander energy resolution on unnecessary position resolution. • Thus we want to confine the position information to only a small slice of the bandwidth at high frequencies. Both sensors ultimately measure the same temperature increase, but they experience different thermalization delays.

So, how cold do we need to go?

It depends on the detector technology, but basically the 10 mK to 100 mK range. XRS and XQC have heat sink temperatures of 65 mK. The Constellation-X baseline is 50 mK.

How do you get that cold on a satellite?

The most straightforward way is to use an adiabatic demagnetization refrigerator (ADR).

The XRS on-orbit duty cycle was expected to be 97% (1 hour for recharge needed every 36 hours). Some Constellation-X designs include multi-stage ADRs that switch between salt pills to provide continuous cooling.

In XRS, the discharge thermal sink is provided by liquid helium (pumped by the vacuum of space). A guard dewar of solid neon extends the lifetime of this helium.

Low temperature detectors and x-ray astronomy:

XQC – 1996, 1999, …

XRS – launch failure in 2000, reflight in 200532 pixel calorimeter array

Constellation-X – 201032 x 32 pixel calorimeter array

XEUS – 2015?calorimeters or STJ

Undoubtedly others in between, to be defined…

The x-ray sky in soft x-ray emission

Results for 140 seconds of observation time

XQC

• Goddard 32-pixel

XRSarray :• 8 - 9 eV baseline and low energies• 9 - 10 eV at 3.3 keV• 11 - 12 eV at 5.9 keV

Engineering Model XRS detector system incorporated into compact laboratory ADR dewar

Microcalorimeter connected to EBIT at the Lawrence Livermore National Laboratory

Basic atomic physics measurements.

Application of XRS under real conditions of complex, time-dependent spectra.

Laboratory Astrophysics with XRS Hardware

Every 5 seconds, slightly ionized atoms (+1, +2) are injected into the trap.

Once there, these atoms are further ionized by the EBIT electron beam toward an equilibrium state determined by the beam energy.

Creating an Ionized Plasma with EBIT

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Photon Energy (keV)

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Photon energy (keV)

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E = 3.0 keVbeam

Broad-band Calorimeterspectrum

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Laboratory Astrophysics using Microcalorimeter

EBIT - Fe ions

Simulating Thermal Plasmas with EBIT

Vary electron beam energy as a function of time so that it time averages out to a Maxwellian energy distribution with a specified <kT>.

The sweep cycle is faster than ionization and recombination timescales. We repeat the cycle many times over a period of several seconds.

We have completed a first survey from <kT>=0.5 keV to 3 keV

Bea

m E

nerg

y (k

eV)

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• Low temperature detectors are being developed for imaging spectroscopy.

• The choice of detector for a given application depends on the measurement priorities. Calorimeters will tend towards higher resolution. Non-calorimetric devices will tend towards higher speeds. Beyond that very generic (and not particularly useful) statement, the suitability of a detector comes down to how well it can actually be implemented with real materials and real read-out electronics in a practical cryostat.

• Detector concepts may fall out of favor, and new ideas may gain popularity, but sensitive energy resolving detectors will always require LOW TEMPERATURES. Thus, we need cold detectors to study the hot universe.

Summary and comparisons: